How to uv unwrap a curved pipe?
Final:




Overview:

Seems:

This is how I have placed them, not ideal. Seem should be marked along middle edge for a better result. Just count them and select right one.



Unwrapping:

Use my answer from here and don't skip any step. This is crucial.

https://blender.stackexchange.com/a/78362/29370 

Correcting UV:

Now you should have nice straight UV map.


Select middle edge (or edges).





Turn on Proportional Editing and change Falloff type to Linear.





Move selected edges on X axis to minimise stretching. Don't forget to use Falloff scale - MouseWheel.